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A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - S l o g | P | d σ ) : P a polynomial in n , where S denotes the euclidean unit sphere in n and σ its unitary surface measure.

A Hilbert Lemniscate Theorem in 2

Thomas Bloom, Norman Levenberg, Yu. Lyubarskii (2008)

Annales de l’institut Fourier

For a regular, compact, polynomially convex circled set K in C 2 , we construct a sequence of pairs { P n , Q n } of homogeneous polynomials in two variables with deg P n = deg Q n ...

A new characterization of the analytic surfaces in 3 that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that an analytic surface V in a neighborhood of the origin in 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in 3 and each d 1 , the (algebraic) limit variety T γ , d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k -dimensional analytic variety V to satisify PL loc .

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